二维电磁逆散射问题的时域高斯-牛顿反演算法  

A time-domain Gauss-Newton inversion algorithm for solving two-dimensional electromagnetic inverse scattering problems

作　　者：刘广东[1] 张开银[1] 

机构地区：[1]阜阳师范学院,物理与电子科学学院,阜阳236037

出　　处：《物理学报》2014年第3期108-122,共15页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:61071022,51271059);安徽省自然科学基金(批准号:1308085MA13);安徽省科技计划项目(批准号:12010302080);阜阳师范学院重点基金(批准号:2011FSKJ01ZD)资助的课题~~

摘　　要：为了直接利用超宽带(UWB)时域测量数据,同时重建二维(2D)目标(OI)的介电常数和电导率,本文将频域高斯-牛顿反演(GNI)算法发展为时域形式.迭代重建过程中,正问题由时域有限差分(FDTD)法求解,而逆问题的病态特性用自适应正则化技术抑制.四类数值算例中,噪声影响均被考虑,仿真结果初步证实了改进算法的可行性和鲁棒性.重建图像呈现超分辨率(SR),有望应用到早期乳腺癌检测等实际问题中.The Gauss-Newton inversion （GNI）, an iterative algorithm, is developed from the frequency domain to the time domain in order to simultaneously reconstruct the electrical permittivity and electric conductivity of a two-dimensional object of interest by directly using the ultra-wideband time-domain measurement data. The resulting forward problem is solved by the finite difference time domain method, while the ill-posedness of the corresponding inverse problem is restrained by an adaptive regularization technique at each iteration. Furthermore, the modified GNI algorithm is applied to four types of numerical examples where a noise model is considered, and the simulated results preliminarily demonstrate its feasibility and robustness. The reconstructed images present super resolution, thus it is expected to be used in the engineering practice such as the detection of the early-stage breast cancer.

关 键 词：电磁逆散射 高斯一牛顿反演 时域有限差分 正则化 

分 类 号：O441.4[理学—电磁学]